Question

What are the main concepts of algebraic expressions and identities

Answer 1

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations. (addition, subtraction, etc.).
Example: $3x+4y–7,4x–10$

The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials.

$(a+b{)}^2=a^2+2ab+b^2$
It is true for all the values of $a$ and $b$

Some identities are:

$(a+b{)}^2=a^2+2ab+b^2$

$(a-b{)}^2=a^2-2ab+b^2$

$(a+b{)}^3=a^3+b^3+3ab(a+b)=a^3+b^3+3a^{2}b+3a{b}^2$

$(a+b{)}^3=a^3-b^3-3ab(a-b)=a^3-b^3-3a^{2}b+3a{b}^2$

$(a+b)(a–b)=a^2–b^2$

$(x+a)(x+b)=x^2+(a+b)x+ab$